Question
Solve for \( s \). \( 125 s^{3}-27=0 \) Write your answers in simplified, rationalized form. Submit
Ask by Harrington Alexander. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( s = \frac{3}{5} \)
Solution
Solve the equation \( 125s^{3}-27=0 \).
Solve the equation by following steps:
- step0: Solve for \(s\):
\(125s^{3}-27=0\)
- step1: Move the constant to the right side:
\(125s^{3}=0+27\)
- step2: Remove 0:
\(125s^{3}=27\)
- step3: Divide both sides:
\(\frac{125s^{3}}{125}=\frac{27}{125}\)
- step4: Divide the numbers:
\(s^{3}=\frac{27}{125}\)
- step5: Simplify the equation:
\(\sqrt[3]{s^{3}}=\sqrt[3]{\frac{27}{125}}\)
- step6: Calculate:
\(s=\sqrt[3]{\frac{27}{125}}\)
- step7: Simplify the root:
\(s=\frac{3}{5}\)
The solution to the equation \(125s^{3}-27=0\) is \(s=\frac{3}{5}\) or \(s=0.6\).
Reviewed and approved by the UpStudy tutoring team
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Beyond the Answer
To solve the equation \( 125 s^{3} - 27 = 0 \), we first isolate \( s^{3} \): \[ 125 s^{3} = 27 \] Next, we divide both sides by 125 to get: \[ s^{3} = \frac{27}{125} \] Now, we take the cube root of both sides: \[ s = \sqrt[3]{\frac{27}{125}} = \frac{\sqrt[3]{27}}{\sqrt[3]{125}} = \frac{3}{5} \] Thus, the solution in simplified form is: \[ s = \frac{3}{5} \]